The minimal free resolution of a certain determinantal ideal

Eun J. Choi; Young H. Kim; Hyoung J. Ko; Seoung J. Won

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2005; 20(2): 275-290

Printed June 1, 2005

The minimal free resolution of a certain determinantal ideal

Eun J. Choi, Young H. Kim, Hyoung J. Ko, Seoung J. Won

Yonsei University, Yonsei University, Yonsei University, Yonsei University

Abstract

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Abstract

Let $S=R[x_{ij}|1\leq i \leq m, 1\leq j \leq n]$ be the polynomial ring over a noetherian commutative ring $R$ and $I_p$ be the determinantal ideal generated by the $p \times p$ minors of the generic matrix $(x_{ij})(1 \leq p \leq \min(m,n)).$ We describe a minimal free resolution of $S/I_p,$ in the case $m=n=p+2$ over $\Bbb Z.$

Keywords: determinantal ideal, minimal free resolution

MSC numbers: 13C40